For Israel's prime minister, Binyamin Netanyahu, last week should have been about repairing the diplomatic bridges damaged in a series of international encounters. After visiting Canada at the start of the week, the acerbic leader's next stop was to have been the crucial one – a visit to Washington to meet President Barack Obama.

This meeting was intended to heal the wounds caused by Israel's announcement in March – in defiance of the US – that it planned to build large new settlements in the territories that it had occupied since the Six Day War in 1967. The plan was announced as US vice president Joe Biden arrived in Israel. It was a calculated diplomatic snub, Netanyahu was told at the time, that had "humiliated" the US president.

As things turned out, Netanyahu didn't make it to Washington. Relations now, if anything, are frostier than ever.What put an end to Netanyahu's trip is now well documented. At 4.30am on Sunday, dozens of Israeli naval commandos in Operation Sea Breeze boarded a flotilla of ships attempting to run Israel's blockade of Gaza and deliver aid. The mission left a trail of dead and wounded among the 600 activists on the lead ship, the Turkish flagged Mavi Marmara.

As news emerged of the disastrous raid, Netanyahu – who was staying at the official residence of Stephen Harper, the Canadian prime minister – found himself convening an all-night meeting with his team to calculate Israel's response to the wave of international condemnation. If Netanyahu and his senior advisers hoped the Marmara incident would quickly blow over, they were wrong.

The revelation that many of those killed – eight Turks and a US-Turkish citizen – were shot in the head at close range by members of Israel's Shayetet 13 naval special forces team only exacerbated the sense of anger in many quarters, above all in Turkey.

And while Israeli diplomats and ministers have tried to spin the clash on the aid flotilla as either much ado about nothing, or as a justified response to violent and illegal actions by the activists, the diplomatic fallout is threatening to dwarf the international reaction to Israel's war against Gaza last year.

Israel's relationship with its closest Muslim ally, Turkey, has been pronounced fatally wounded. A succession of European leaders, including David Cameron and Nicolas Sarkozy, have lined up to pronounce Israel's long-term embargo of Hamas-run Gaza as unsustainable and indefensible. Most serious of all for Netanyahu, Israel's closest and most assiduous ally, the United States, has also endorsed that view, going out of its way to reveal that it had warned Jerusalem to show restraint when dealing with the six-ship convoy.

Behind the inevitable bluster, the real question many Israelis are now asking is: how did it come to this? The answer is that the bungled raid on the Mavi Marmara has been a powerful catalyst for the escalating sense of repugnance at Israel's policy of collective punishment of the 1.5 million residents of Gaza, while sharply underlining the perception of the intransigence of Israel under Netanyahu. It has also exposed how slow Israel's leadership has been to appreciate the profound changes that it faces on the regional and international stage – and how it should respond to them.

Those changes were most starkly visible last week in Turkey. Prime Minister Recep Tayyip Erdogan expressed it most forcefully in a televised speech last week: "You [Israel] killed 19-year-old Furkan Dogan brutally. Which faith, which holy book can be an excuse for killing him? I am speaking to them in their own language. The sixth commandment says, 'Thou shalt not kill'. Did you not understand? I'll say again. I say in English, 'You shall not kill'. Did you still not understand? So I'll say to you in your own language. I say in Hebrew, 'Lo Tirtzakh'."

But if the assault on a Turkish-flagged ship, supported by a Turkish organisation, which led to the deaths of Turkish citizens, has been a major source of anger, it has not been the only one. Another has been the sense that Israel has taken the relationship with Turkey as a "given", even as the Nato member has sought to assert its increasing leadership in the Muslim world and as a bridge between east and west.

In recent years, an increasingly confident Turkey has denied the US permission to transport troops through its territory en route to the invasion of Iraq, and has pressed for a seat on the UN Security Council. It has attempted mediation between Syria and Israel, while trying to build alliances with Iraq and Iran. And it has used its position as Israel's closest military ally in the Muslim world to launch increasingly sharp criticism of the Jewish state – not least over Gaza.

But if Turkey's growing influence on the world stage has been recognised in the US as valuable, with recent visits both by secretary of state Hillary Clinton and Middle East envoy George Mitchell, that message has been missed in Israel.

That is certainly one problem, but it has not been the only one. The Mavi Marmara incident has also directed a harsh light on the country's increasingly fraught relationship with America. And while many commentators in Israel last week were lamenting that the real problem was that they had failed to adequately explain themselves over the attack on the Mavi Marmara – and that bad diplomacy was really to blame – some at least have begun to recognise that unconditional US support should not be taken for granted.

They include the head of Israel's foreign intelligence service, who warned that his country was "gradually turning from an asset of the United States to a burden".

That fear has been fuelled by the White House's attempts to strike a far sterner tone with Israel, a position that was evident before the flotilla crisis, when it was revealed that US officials had repeatedly pressed Israel not to over-react to the approach of the sea convoy to Gaza's shores.

"We communicated with Israel through multiple channels many times regarding the flotilla. We emphasised caution and restraint, given the anticipated presence of civilians, including American citizens," a State Department spokesman said in a statement.

Other US officials, in off-the-record briefings and leaked comments to American newspapers, also have aired their frustrations with Israel's conduct. "There is no question that we need a new approach to Gaza," one official told the New York Times. That echoed comments by Hillary Clinton, who, immediately after the attack on the flotilla, called the situation in Gaza "unsustainable".

That approach – of trying to get Israel to soften its attitude – has come as no great surprise to many Middle East watchers in Washington. "It does not surprise me that the Obama administration is trying to urge Israel to better manage this," said Danielle Pletka, vice president for foreign and defence policy studies at the American Enterprise Institute. "The administration has tried to manage this mess. They have tried hard to extricate Israel from the fiasco."

Speaking to the Washington Post yesterday, Daniel Kurtzer, the former US ambassador to Israel, argued the problem was more fundamental. "[Israelis] look at the world quite differently from the way from this president does, and they are not willing to just fall in line because he is the president. Israel and the United States are seeing the threat environment in the region… in increasingly different ways. And for the United States, that means Israel is a problem, as an ally heading in a very different direction."

All of which leaves an isolated Israel in a deep dilemma, made all the more difficult because many Israelis do not understand the reason for the outrage. "It's good that they filmed it at least," says one Israeli woman at Jerusalem's Hebrew university gym last week, commenting on the footage of the assault playing on the screens overhead – a video clip released by the Israeli army which shows the activists attacking the Israeli troops with clubs and iron bars as they arrive on deck, claimed as evidence of a premeditated, violent attack.

Her friend, also watching, says: "But you know, I heard that overseas they still don't believe us." The first woman lets out an exasperated gasp. "How is that possible?" she asks.

That, in microcosm, is the result of the assault on the flotilla – a widening chasm between Israel's view of its actions and the way they are seen around the world. Because the army is conscripted, Israeli society and its military are intimately bound and, as a consequence, the army is trusted to tell the truth. What raises more eyebrows is the accompanying inability to see why the Israeli perspective on events might not echo globally.

In Israel, there is one explanation for rising hostility. "What we are seeing around the flotilla incident is just an extension of something which has been there for some time," says Danny Gillerman, former Israeli ambassador to the UN. "It is an outrageous hypocrisy and double standard to revile Israel for these actions, when other countries in the same situation would do exactly the same, if not worse."

Gillerman dismisses other nations' anger that their citizens had been shot dead, hospitalised, or held without contact with the outside world at an Israeli desert prison facility. " 'Foreign nationals' or 'human rights activists' are broadly and wrongly used terms," he says. "They were using clubs, trying to lynch and mob our soldiers."

He does not hold Israel responsible for the now deteriorating relations with Turkey. "[The flotilla] was organised by extreme, Islamic terror groups connected to al-Qaida and supported by the Turkish prime minster, who for some time has been steering his country into the arms of Iran and Syria," says Gillerman. "At the end of the day, it is up to Erdogan to decide if he wants to be part of the western world."

Israeli politicians and analysts say that the country needs to fight harder on the diplomatic front, to redress the imbalance of opinion against the nation. Labour MP Einat Wilf raised this issue in Israel's parliament last week.

"Israel is being threatened in two arenas," she says. "One is military, with which we are familiar and experienced, but the other one is intellectual, the arena in which the very idea that the Jewish people have the right to a homeland is attacked." She sees the flotilla as falling into that category.

Outside Israel, the flotilla is viewed very differently indeed: as a challenge to Israel's stranglehold on Gaza, and as having been responsible for widespread awareness of an untenable siege. It is that which Israel cannot see.

And while Israel might not be able to break with its disconnected world view, it may yet be forced to break the blockade on Gaza.